14n^2-82n+60=0

Solution for 14n^2-82n+60=0 equation:

Simplifying
14n2 + -82n + 60 = 0

Reorder the terms:
60 + -82n + 14n2 = 0

Solving
60 + -82n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -41n + 7n2) = 0

Factor a trinomial.
2((6 + -7n)(5 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.8571428571, 5}